Questions on Series
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(1.) Determine the sums of these infinite series.
$ (a.)\;\; \sum\limits_{n = 1}^\infty \dfrac{7}{2^n} \\[5ex] (b.)\;\; \sum\limits_{n = 1}^\infty \left(\dfrac{1}{2^n} - \dfrac{1}{2^{n + 1}}\right) \\[5ex] (c.)\;\; \sum\limits_{n = 1}^\infty \left(\dfrac{1}{2^n} - \dfrac{1}{2^{n - 1}}\right) \\[5ex] $
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(2.) For the series: $\sum\limits_{n = 1}^\infty \left(-\dfrac{3}{5}\right)^{n - 1}$
(a.) Identify the type of series.
(b.) Determine whether it converges or diverges.
(c.) If it converges, calculate the sum.
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(3.)
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